An LQP-Based Symmetric Alternating Direction Method of Multipliers with Larger Step Sizes

作     者：Zhong-Ming Wu Min Li 

作者机构：School of Economics and ManagementSoutheast UniversityNanjing 210096China School of Management and EngineeringNanjing UniversityNanjing 210093China 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2019年第7卷第2期

页      面：365-383页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This research was supported by National Natural Science Foundation of China Grant 11771078 Natural Science Foundation of Jiangsu Province Grant BK20181258 Project of 333 of Jiangsu Province Grant BRA2018351 Postgraduate Research&Practice Innovation Program of Jiangsu Province Grant KYCX18_0200 

主　　题：Convex optimization Symmetric alternating direction method of multipliers Logarithmic-quadratic proximal regularization Larger step sizes Global convergence 

摘      要：Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization *** method updates the Lagrange multiplier twice with appropriate step sizes at each ***,such step sizes were conservatively shrunk to guarantee the convergence in recent *** this paper,we are devoted to seeking larger step sizes whenever *** logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ***,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size ***,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.